A mass M is initially at rest on a horizontal surface, μs=0.30 and μk=0.20 . A horizontal string then pulls M with a tension T. Forces below are magnitudes. Indicate if each statement is correct or incorrect

If M does not accelerate, then T ≤ μsN
M will accelerate if T exceed μsN
The NET force on M (if M does not move) is T
N equals Mg
T equals μsN if M remains at rest
M will accelerate if T exceeds μkN

To determine the correctness of each statement, let's break down the given information and use Newton's laws of motion.

1. If M does not accelerate, then T ≤ μsN
Correct. According to Newton's laws of motion, if an object is not accelerating, the net force acting on it is zero. In this case, the tension force T must be less than or equal to the product of the coefficient of static friction μs and the normal force N. This ensures that the static friction can balance out the applied force T, preventing acceleration.

2. M will accelerate if T exceeds μsN
Incorrect. If T exceeds μsN, the static friction will be overcome, causing the object to start moving. However, since the statement mentions that M will accelerate, it is assuming that T continues to exceed μsN even after the object is set in motion. In reality, once the object starts moving, it experiences kinetic friction, which is generally weaker than static friction. Therefore, the acceleration may decrease.

3. The net force on M (if M does not move) is T
Incorrect. If M does not move, this implies that the object is in equilibrium, and the net force acting on it must be zero. In this situation, the net force will consist of both the force of tension T and the static friction force, which balances out the applied force. Therefore, the correct statement would be that the net force on M, in this case, is zero.

4. N equals Mg
Correct. The normal force N is equal to the product of the mass of the object M and the acceleration due to gravity, commonly denoted as g. Hence, N = Mg.

5. T equals μsN if M remains at rest
Correct. The tension force T can be equal to the product of the coefficient of static friction μs and the normal force N if the object remains at rest. This is the maximum limiting value for T before the object starts moving. Thus, if T exceeds μsN, the object will initiate motion and kinetic friction will come into play.

6. M will accelerate if T exceeds μkN
Correct. If T exceeds μkN, where μk is the coefficient of kinetic friction, the object will experience a net applied force. This will cause it to accelerate, given that the magnitude of the force due to friction (μkN) is less than T.